In [1]:
import cupy as cp
import numpy as np
from time import perf_counter
from pyqcu import define
from pyqcu import io
from pyqcu import qcu
import cupyx.scipy.sparse.linalg as csla
from typing import Callable, Tuple, List

print('My rank is ', define.rank)
    @@@@@@######QCU NOTES START######@@@@@@@
    1. The libqcu.so was compiled when pyqcu setup in download_path/PyQCU/lib, please add this path to your LD_LIBRARY_PATH.
    2. The QCU(PyQCU) splite grid by x->y->z->t, lattice by x->y->z->t->p->d->c->c or x->y->z->t->c->s(->p) and x->y->z->t->c->s->c->s(->p).
    3. The QUDA(PyQUDA) splite grid by t->z->y->x, lattice by c->c->x->y->z->t->p->d or c->s->x->y->z->t(->p) and c->s->c->s->x->y->z->t(->p).
    4. The QCU input params in numpy array(dtype=np.int32), argv in  numpy array(dtype=np.float32 or float64) array, set_ptrs in numpy array(dtype=np.int64), other in cupy array(dtype=cp.complex64 or complex128).
    5. The smallest lattice size is (x=4,y=4,z=4,t=8) that QCU support.
    @@@@@@######QCU NOTES END######@@@@@@@
    
My rank is  0
In [ ]:
params = np.array([0]*define._PARAMS_SIZE_, dtype=np.int32)
params[define._LAT_X_] = 32
params[define._LAT_Y_] = 32
params[define._LAT_Z_] = 32
params[define._LAT_T_] = 32
params[define._LAT_XYZT_] = 1048576
params[define._GRID_X_] = 1
params[define._GRID_Y_] = 1
params[define._GRID_Z_] = 1
params[define._GRID_T_] = 1
params[define._PARITY_] = 0
params[define._NODE_RANK_] = 0
params[define._NODE_SIZE_] = 1
params[define._DAGGER_] = 0
params[define._MAX_ITER_] = 1e4
params[define._DATA_TYPE_] = 0
params[define._SET_INDEX_] = 2
params[define._SET_PLAN_] = 0
argv = np.array([0.0]*define._ARGV_SIZE_, dtype=np.float32)
argv[define._MASS_] = 0.0
argv[define._TOL_] = 1e-9
print("Parameters:", params)
print("Arguments:", argv)
Parameters: [     32      32      32      32 1048576       1       1       1       1
       0       0       1       0   10000       0       2       0]
Arguments: [0.e+00 1.e-09]
In [3]:
gauge_filename = f"quda_wilson-dslash-gauge_-{params[define._LAT_X_]}-{params[define._LAT_Y_]}-{params  [define._LAT_Z_]}-{params[define._LAT_T_]}-{params[define._LAT_XYZT_]}-{params[define._GRID_X_]}-{params[define._GRID_Y_]}-{params[define._GRID_Z_]}-{params[define._GRID_T_]}-{params[define._PARITY_]}-{params[define._NODE_RANK_]}-{params[define._NODE_SIZE_]}-{params[define._DAGGER_]}-f.bin"
print("Gauge filename:", gauge_filename)
gauge = cp.fromfile(gauge_filename, dtype=cp.complex64,
                    count=params[define._LAT_XYZT_]*define._LAT_DCC_)
gauge = io.gauge2ccdptzyx(gauge, params)
print("Gauge:", gauge)
print("Gauge data:", gauge.data)
print("Gauge shape:", gauge.shape)
Gauge filename: quda_wilson-dslash-gauge_-32-32-32-32-1048576-1-1-1-1-0-0-1-0-f.bin
U: [ 0.9888613 +0.02130369j  0.07348315-0.02076806j -0.09857995+0.07842391j
 -0.07511304-0.01086277j  0.9932049 -0.00666964j  0.04573338+0.07515373j
  0.10230845+0.07397576j -0.03536638+0.08011071j  0.9880291 -0.01380186j]
_U: [ 0.        +0.j          0.        +0.j          0.        +0.j
  0.        +0.j          0.        +0.j          0.        +0.j
  0.10230846+0.07397576j -0.03536638+0.08011071j  0.9880291 -0.01380186j]
Gauge: 37748736
Gauge: [[[[[[[[ 9.88861322e-01+2.13036854e-02j
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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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     ...


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         9.95830059e-01-2.89488360e-02j ...
         9.69687998e-01-2.33844340e-01j
         9.73142028e-01+8.84055793e-02j
         9.76351976e-01-1.37854680e-01j]]

      ...

      [[ 9.97041166e-01-2.33190898e-02j
         9.81663465e-01+1.68743834e-01j
         9.92810726e-01+7.69913569e-02j ...
         9.91827130e-01-9.46760084e-03j
         9.82575357e-01-1.01889715e-01j
         9.91184592e-01-4.83878739e-02j]
       [ 9.92326736e-01+9.60645154e-02j
         9.91317511e-01-3.56840976e-02j
         9.92937088e-01-4.93157916e-02j ...
         9.94010031e-01+4.87456471e-02j
         9.93812442e-01+1.65337194e-02j
         9.84295368e-01-5.51280901e-02j]
       [ 9.87445116e-01+8.13022535e-03j
         9.91929889e-01+9.69947502e-02j
         9.89831090e-01+1.71946976e-02j ...
         9.92597640e-01+4.77729365e-02j
         9.99109566e-01+1.62187666e-02j
         9.94775236e-01+1.56874470e-02j]
       ...
       [ 9.65493917e-01-1.50908813e-01j
         9.69291031e-01+7.31750578e-02j
         9.92072284e-01+2.26269523e-03j ...
         9.92003024e-01+8.94998387e-02j
         9.68693852e-01-1.35457143e-01j
         9.92689788e-01+6.65792301e-02j]
       [ 9.63562071e-01-1.34147942e-01j
         9.87656713e-01-2.97176745e-03j
         9.71306086e-01-5.56050241e-03j ...
         9.70454276e-01+1.19548365e-01j
         9.85312223e-01-8.92719626e-02j
         9.76129591e-01+6.03280738e-02j]
       [ 9.90023911e-01+5.19349687e-02j
         9.96814549e-01+1.28967129e-02j
         9.86090362e-01+5.48941270e-02j ...
         9.87902701e-01-1.52926231e-02j
         9.89921272e-01+4.95315380e-02j
         9.85276461e-01-5.22483774e-02j]]

      [[ 9.96478260e-01+3.82887162e-02j
         9.94808912e-01-3.73382270e-02j
         9.97911274e-01-2.74260510e-02j ...
         9.84751225e-01-6.45348579e-02j
         9.91316319e-01+2.30151787e-02j
         9.71297026e-01+1.21417291e-01j]
       [ 9.90487158e-01-9.97319967e-02j
         9.97269154e-01+4.09824811e-02j
         9.93274093e-01-6.83204755e-02j ...
         9.74156499e-01+1.66722655e-01j
         9.96088922e-01+6.14344552e-02j
         9.75944340e-01+1.80472195e-01j]
       [ 9.80137825e-01-3.25242057e-02j
         9.96238589e-01-8.19443166e-03j
         9.83536959e-01-4.05329764e-02j ...
         9.72300410e-01+1.11450464e-01j
         9.70654726e-01-1.63155526e-01j
         9.92724180e-01+4.18733358e-02j]
       ...
       [ 9.74617958e-01+1.67996828e-02j
         9.82483387e-01+5.70351146e-02j
         9.66885984e-01+1.75825179e-01j ...
         9.87893879e-01+1.53177381e-02j
         9.84604776e-01-5.83510334e-03j
         9.87243831e-01+1.26613289e-01j]
       [ 9.90917504e-01+3.77910696e-02j
         9.87498939e-01-1.23531550e-01j
         9.95261848e-01+5.42504042e-02j ...
         9.85861957e-01-2.74544880e-02j
         9.83909309e-01+1.07454151e-01j
         9.95772123e-01-5.45856729e-03j]
       [ 9.80439007e-01-1.21368796e-01j
         9.92627084e-01-5.12746386e-02j
         9.96057332e-01-5.91591336e-02j ...
         9.98781979e-01-3.18981111e-02j
         9.95732903e-01+6.23967759e-02j
         9.90981519e-01+1.27822720e-03j]]

      [[ 9.83889282e-01-5.33840954e-02j
         9.93013024e-01-2.68412679e-02j
         9.87258911e-01-1.45019397e-01j ...
         9.75535095e-01+1.37851059e-01j
         9.79064286e-01-3.43752354e-02j
         9.87260044e-01-1.12760914e-02j]
       [ 9.96899784e-01-5.62877133e-02j
         9.83844161e-01-4.56487797e-02j
         9.79288578e-01-5.00736665e-03j ...
         9.87465262e-01+4.23426181e-02j
         9.96232331e-01-2.79147569e-02j
         9.93339241e-01+9.58476914e-04j]
       [ 9.79844570e-01-4.22503706e-03j
         9.80435312e-01-4.30875234e-02j
         9.86860037e-01-1.23507664e-01j ...
         9.82289970e-01+1.57409191e-01j
         9.78417695e-01+1.98838543e-02j
         9.69375253e-01-1.06659710e-01j]
       ...
       [ 9.91334558e-01+5.89914247e-03j
         9.89599168e-01+1.08037837e-01j
         9.92483735e-01-2.71785613e-02j ...
         9.83042955e-01+6.85607046e-02j
         9.85138893e-01-1.03230432e-01j
         9.94926035e-01+4.62608375e-02j]
       [ 9.96221125e-01-4.49398458e-02j
         9.94287491e-01+3.47633362e-02j
         9.93404090e-01-8.02222863e-02j ...
         9.69325900e-01-4.79393899e-02j
         9.92115915e-01-5.35401218e-02j
         9.92409110e-01+2.44176984e-02j]
       [ 9.79039073e-01+1.51826754e-01j
         9.86636817e-01-6.89331144e-02j
         9.79794681e-01+8.45923647e-02j ...
         9.84965742e-01-4.14918251e-02j
         9.85355198e-01-4.42222990e-02j
         9.93500471e-01-6.05962276e-02j]]]]]]]]
Gauge data: <MemoryPointer 0xb05600000 device=0 mem=<cupy.cuda.memory.PooledMemory object at 0x7fcc564bcd70>>
Gauge shape: (3, 3, 4, 2, 32, 32, 32, 16)
In [4]:
set_ptrs = np.array(params, dtype=np.int64)
print("Set pointers:", set_ptrs)
print("Set pointers data:", set_ptrs.data)
qcu.applyInitQcu(set_ptrs, params, argv)
Set pointers: [     32      32      32      32 1048576       1       1       1       1
       0       0       1       0   10000       0       2       0]
Set pointers data: <memory at 0x7fcc553b2980>
gridDim.x               :4096
blockDim.x              :128
host_params[_LAT_X_]    :16
host_params[_LAT_Y_]    :32
host_params[_LAT_Z_]    :32
host_params[_LAT_T_]    :32
host_params[_LAT_XYZT_] :524288
host_params[_GRID_X_]   :1
host_params[_GRID_Y_]   :1
host_params[_GRID_Z_]   :1
host_params[_GRID_T_]   :1
host_params[_PARITY_]   :0
host_params[_NODE_RANK_]:0
host_params[_NODE_SIZE_]:1
host_params[_DAGGER_]   :0
host_params[_MAX_ITER_] :10000
host_params[_SET_INDEX_]:2
host_params[_SET_PLAN_] :0
host_argv[_MASS_]       :0.000000e+00
host_argv[_TOL_]        :1.000000e-09
lat_2dim[_XY_]          :512
lat_2dim[_XZ_]          :512
lat_2dim[_XT_]          :512
lat_2dim[_YZ_]          :1024
lat_2dim[_YT_]          :1024
lat_2dim[_ZT_]          :1024
lat_3dim[_YZT_]         :32768
lat_3dim[_XZT_]         :16384
lat_3dim[_XYT_]         :16384
lat_3dim[_XYZ_]         :16384
lat_4dim                :524288
grid_2dim[_XY_]         :1
grid_2dim[_XZ_]         :1
grid_2dim[_XT_]         :1
grid_2dim[_YZ_]         :1
grid_2dim[_YT_]         :1
grid_2dim[_ZT_]         :1
grid_3dim[_YZT_]        :1
grid_3dim[_XZT_]        :1
grid_3dim[_XYT_]        :1
grid_3dim[_XYZ_]        :1
grid_index_1dim[_X_]    :0
grid_index_1dim[_Y_]    :0
grid_index_1dim[_Z_]    :0
grid_index_1dim[_T_]    :0
move_wards[_B_X_]       :0
move_wards[_B_Y_]       :0
move_wards[_B_Z_]       :0
move_wards[_B_T_]       :0
move_wards[_F_X_]       :0
move_wards[_F_Y_]       :0
move_wards[_F_Z_]       :0
move_wards[_F_T_]       :0
move_wards[_BX_BY_]     :0
move_wards[_BX_BZ_]     :0
move_wards[_BX_BT_]     :0
move_wards[_BY_BZ_]     :0
move_wards[_BY_BT_]     :0
move_wards[_BZ_BT_]     :0
move_wards[_FX_BY_]     :0
move_wards[_FX_BZ_]     :0
move_wards[_FX_BT_]     :0
move_wards[_FY_BZ_]     :0
move_wards[_FY_BT_]     :0
move_wards[_FZ_BT_]     :0
move_wards[_BX_FY_]     :0
move_wards[_BX_FZ_]     :0
move_wards[_BX_FT_]     :0
move_wards[_BY_FZ_]     :0
move_wards[_BY_FT_]     :0
move_wards[_BZ_FT_]     :0
move_wards[_FX_FY_]     :0
move_wards[_FX_FZ_]     :0
move_wards[_FX_FT_]     :0
move_wards[_FY_FZ_]     :0
move_wards[_FY_FT_]     :0
move_wards[_FZ_FT_]     :0
set_ptr:0x55619355e2a0
long long set_ptr:93877572068000
lattice set init total time:0.048005424 sec
In [5]:
# give x, b, r, r_tilde, p, v, s, t
lat_t = params[define._LAT_T_]
lat_z = params[define._LAT_Z_]
lat_y = params[define._LAT_Y_]
lat_x = int(params[define._LAT_X_]/define._LAT_P_)
lat_d = define._LAT_D_
lat_s = define._LAT_S_
lat_p = define._LAT_P_
lat_c = define._LAT_C_
latt_shape = (lat_s, lat_c, lat_t, lat_z, lat_y, lat_x)
MAX_ITER = params[define._MAX_ITER_]
TOL = argv[define._TOL_]
N = params[define._LAT_XYZT_] * define._LAT_HALF_SC_
In [6]:
def _matvec(src, eigen_value=0.0):
    print("norm src", cp.linalg.norm(src))
    dest = cp.zeros(N, cp.complex64)
    qcu.applyWilsonCgDslashQcu(dest, src, gauge, set_ptrs, params)
    print("norm dest", cp.linalg.norm(dest))
    return dest-src*eigen_value
In [7]:
# def power_iteration(matvec, v0, num_iter=params[define._MAX_ITER_], tol=argv[define._TOL_]):
#     v = v0
#     prev_v = cp.zeros_like(v)
#     for i in range(num_iter):
#         Av = matvec(v)
#         v_new = Av / cp.linalg.norm(Av)
#         diff = cp.linalg.norm(v_new - v)
#         print(f"Iteration {i+1}: difference = {diff:.6e}")
#         if diff < tol:
#             print(
#                 f"Power Iteration converged after {i+1} iterations. Difference: {diff:.6e}")
#             break
#         v = v_new
#     eigenvalue = cp.dot(v.conj().T, matvec(v))
#     return eigenvalue, v
# def validate_power_iteration():
#     v0 = cp.random.randn(N).astype(cp.complex64)
#     eigenvalue, eigenvector = power_iteration(_matvec, v0)
#     print("Dominant eigenvalue:", eigenvalue)
#     print("Corresponding eigenvector:", eigenvector[:10])
#     Ax = _matvec(eigenvector)
#     eigenvalue_check = cp.dot(eigenvector.conj().T, Ax)
#     print(f"Eigenvalue verification (v^T A v): {eigenvalue_check}")
#     if cp.isclose(eigenvalue, eigenvalue_check):
#         print("Validation passed: Eigenvalue calculation is correct.")
#     else:
#         print("Validation failed: Eigenvalue calculation is incorrect.")
#     print("Eigenvector norm:", cp.linalg.norm(eigenvector))
#     return eigenvalue, eigenvector
# eigenvalue, eigenvector = validate_power_iteration()
# print("Diff:", cp.linalg.norm(_matvec(eigenvector) -
#       eigenvalue*eigenvector) / cp.linalg.norm(eigenvector))
In [8]:
# # bistabcg
# def dot(a, b):
#     cp.cuda.runtime.deviceSynchronize()
#     return cp.inner(a.flatten().conjugate(), b.flatten())


# def diff(a, b):
#     cp.cuda.runtime.deviceSynchronize()
#     return cp.linalg.norm(a - b) / cp.linalg.norm(b)


# def run(eigen_value):
#     t0 = perf_counter()
#     x = cp.random.rand(N).astype(cp.complex64)
#     print("shape:", x.shape)
#     b = cp.zeros(N, cp.complex64)  # must be zero
#     r = cp.zeros(N, cp.complex64)
#     r_tilde = cp.zeros(N, cp.complex64)
#     p = cp.zeros(N, cp.complex64)
#     s = cp.zeros(N, cp.complex64)
#     v = cp.zeros(N, cp.complex64)
#     t = cp.zeros(N, cp.complex64)
#     r = b - _matvec(x, eigen_value)
#     r_tilde = r
#     r_norm2 = 0
#     rho_prev = 1
#     rho = 0
#     alpha = 1
#     omega = 1
#     beta = 0
#     for i in range(MAX_ITER):
#         # print("## rho:", rho)
#         rho = dot(r_tilde, r)
#         # print("## beta:", beta)
#         beta = (rho / rho_prev) * (alpha / omega)
#         p = r + (p - v * omega) * beta
#         # v = A * p
#         v = _matvec(p, eigen_value)
#         # print("## alpha:", alpha)
#         alpha = rho / dot(r_tilde, v)
#         s = r - v * alpha
#         # t = A * s
#         t = _matvec(s, eigen_value)
#         # print("## omega:", omega)
#         omega = dot(t, s) / dot(t, t)
#         x = x + p * alpha + s * omega
#         r = s - t * omega
#         r_norm2 = cp.linalg.norm(r)
#         print("##{}# r_norm2:{}".format(i, r_norm2))
#         _diff = diff(_matvec(x, 0.0), eigen_value*x)
#         print("diff:", _diff)
#         # break
#         # if (r_norm2 < TOL or i == MAX_ITER - 1):
#         #     print("### turns:", i)
#         #     break
#         if (_diff < TOL or i == MAX_ITER - 1):
#             print("### turns:", i)
#             break
#         rho_prev = rho
#     # print(" diff:", diff(_matvec(x, eigen_value), b))
#     # print("x:", x)
#     t1 = perf_counter()
#     print("Time:", t1-t0)
#     return x, _diff


# eigen_value = eigenvalue
# eigen_vector, _diff = run(eigen_value)
# print("eigen_vector:", eigen_vector)
# print("eigen_vector shape:", eigen_vector.shape)
# print("diff:", _diff)
In [9]:
# print("Difference:", cp.linalg.norm(eigenvector-eigen_vector)/cp.linalg.norm(eigenvector))
In [10]:
# import cupyx.scipy.sparse.linalg as csla
# define._LAT_E_ = 24
# A = csla.LinearOperator((N,
#                         N), matvec=_matvec, dtype=cp.complex64)
# evals, evecs = csla.eigsh(a=A, k=define._LAT_E_, which="SA",
#                           return_eigenvectors=True)
# print("evals:", evals)
# print("evecs:", evecs)
# cp.linalg.norm(_matvec(evecs[:, 0])-evals[0] *
#                evecs[:, 0])/cp.linalg.norm(evals[0]*evecs[:, 0])
In [11]:
def shifted_power_iteration(
    matvec,
    n=N,
    num_eigenvalues=define._LAT_E_,
    max_iter=params[define._MAX_ITER_],
    tol=argv[define._TOL_]
):
    eigenvalues = []
    eigenvectors = []
    # 用于存储中间结果的缓冲区
    v = cp.ndarray((n,), dtype=np.complex64)
    w = cp.ndarray((n,), dtype=np.complex64)
    # 存储累积位移
    total_shift = 0.0
    for k in range(num_eigenvalues):
        # 随机初始化向量
        v[:] = cp.random.rand(n) + 1j * cp.random.rand(n)
        # 对已找到的本征向量进行正交化
        for j in range(k):
            projection = cp.dot(cp.conj(eigenvectors[j]), v)
            v -= projection * eigenvectors[j]
        # 归一化
        v /= cp.linalg.norm(v)
        # 幂迭代
        eigenvalue = None
        for iter_count in range(max_iter):
            # 矩阵向量乘法
            w = matvec(v)
            # 应用位移
            w += total_shift * v
            # 计算瑞利商
            new_eigenvalue = cp.dot(cp.conj(v), w)
            # 归一化
            norm = cp.linalg.norm(w)
            if norm < tol:  # 避免零向量
                v[:] = cp.random.rand(n) + 1j * cp.random.rand(n)
                continue
            w /= norm
            # 检查收敛性
            if eigenvalue is not None:
                _diff = abs(new_eigenvalue - eigenvalue)
                print(f"第 {k} 个本征值的第 {iter_count} 次迭代: {_diff:.8f}")
                if _diff < tol:
                    break
            eigenvalue = new_eigenvalue
            v[:] = w
        # 存储结果并减去位移
        if eigenvalue is not None:
            eigenvalue -= total_shift
            eigenvalues.append(eigenvalue)
            eigenvectors.append(v.copy())
            # 更新位移以找到下一个本征值
            total_shift = eigenvalue.real
    return eigenvalues, eigenvectors


eigenvalues, eigenvectors = shifted_power_iteration(_matvec)
# 验证结果
print("计算得到的本征值:")
for i, ev in enumerate(eigenvalues):
    print(f"λ_{i} = {ev:.8f}")
    # 验证本征向量
    v = eigenvectors[i]
    w = cp.zeros_like(v)
    w = _matvec(v)
    error = cp.linalg.norm(w - ev * v) / cp.linalg.norm(w)
    print(f"相对误差: {error:.2e}")
norm src 
0.99999994
norm dest 0.56334966
norm src 1.0
norm dest 1.202488
第 0 个本征值的第 1 次迭代: 0.90937716
norm src 1.0
norm dest 1.2533623
第 0 个本征值的第 2 次迭代: 0.05600929
norm src 1.0
norm dest 1.2895725
第 0 个本征值的第 3 次迭代: 0.03867626
norm src 0.99999994
norm dest 1.318062
第 0 个本征值的第 4 次迭代: 0.02995741
norm src 1.0
norm dest 1.3416498
第 0 个本征值的第 5 次迭代: 0.02459502
norm src 1.0000001
norm dest 1.361727
第 0 个本征值的第 6 次迭代: 0.02083337
norm src 0.9999999
norm dest 1.3790977
第 0 个本征值的第 7 次迭代: 0.01796985
norm src 0.99999994
norm dest 1.3942907
第 0 个本征值的第 8 次迭代: 0.01568353
norm src 0.9999999
norm dest 1.4076836
第 0 个本征值的第 9 次迭代: 0.01380265
norm src 1.0
norm dest 1.419563
第 0 个本征值的第 10 次迭代: 0.01222658
norm src 1.0
norm dest 1.4301529
第 0 个本征值的第 11 次迭代: 0.01088750
norm src 1.0
norm dest 1.4396331
第 0 个本征值的第 12 次迭代: 0.00973725
norm src 1.0
norm dest 1.4481506
第 0 个本征值的第 13 次迭代: 0.00874174
norm src 1.0
norm dest 1.4558268
第 0 个本征值的第 14 次迭代: 0.00787258
norm src 1.0
norm dest 1.462764
第 0 个本征值的第 15 次迭代: 0.00711024
norm src 0.9999999
norm dest 1.4690484
第 0 个本征值的第 16 次迭代: 0.00643754
norm src 1.0
norm dest 1.4747554
第 0 个本征值的第 17 次迭代: 0.00584280
norm src 0.9999999
norm dest 1.4799484
第 0 个本征值的第 18 次迭代: 0.00531387
norm src 0.99999994
norm dest 1.4846841
第 0 个本征值的第 19 次迭代: 0.00484359
norm src 1.0
norm dest 1.489012
第 0 个本征值的第 20 次迭代: 0.00442421
norm src 1.0
norm dest 1.4929744
第 0 个本征值的第 21 次迭代: 0.00404871
norm src 0.99999994
norm dest 1.49661
第 0 个本征值的第 22 次迭代: 0.00371277
norm src 1.0
norm dest 1.4999527
第 0 个本征值的第 23 次迭代: 0.00341201
norm src 1.0
norm dest 1.5030317
第 0 个本征值的第 24 次迭代: 0.00314164
norm src 1.0
norm dest 1.5058742
第 0 个本征值的第 25 次迭代: 0.00289822
norm src 0.99999994
norm dest 1.5085027
第 0 个本征值的第 26 次迭代: 0.00267935
norm src 1.0
norm dest 1.5109391
第 0 个本征值的第 27 次迭代: 0.00248206
norm src 1.0
norm dest 1.5132014
第 0 个本征值的第 28 次迭代: 0.00230372
norm src 1.0
norm dest 1.515306
第 0 个本征值的第 29 次迭代: 0.00214207
norm src 1.0
norm dest 1.5172681
第 0 个本征值的第 30 次迭代: 0.00199604
norm src 0.99999994
norm dest 1.5191001
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norm src 1.0
norm dest 1.5708677
第 23 个本征值的第 1255 次迭代: 0.00000095
norm src 1.0
norm dest 1.5708688
第 23 个本征值的第 1256 次迭代: 0.00000167
norm src 0.9999999
norm dest 1.5708698
第 23 个本征值的第 1257 次迭代: 0.00000000
计算得到的本征值:
λ_0 = 1.57109463+0.00000000j
norm src 0.99999994
norm dest 1.5710948
相对误差: 3.58e-04
λ_1 = 1.57087529-0.00000000j
norm src 0.99999994
norm dest 1.5708764
相对误差: 8.09e-04
λ_2 = 1.57083738-0.00000000j
norm src 0.99999994
norm dest 1.570838
相对误差: 7.78e-04
λ_3 = 1.57078946-0.00000000j
norm src 0.99999994
norm dest 1.5707906
相对误差: 9.31e-04
λ_4 = 1.57083857+0.00000000j
norm src 1.0
norm dest 1.5708395
相对误差: 8.79e-04
λ_5 = 1.57089174-0.00000000j
norm src 0.9999999
norm dest 1.5708926
相对误差: 7.77e-04
λ_6 = 1.57099640+0.00000000j
norm src 0.9999999
norm dest 1.5709975
相对误差: 7.06e-04
λ_7 = 1.57102144+0.00000000j
norm src 0.9999999
norm dest 1.5710222
相对误差: 6.51e-04
λ_8 = 1.57090056+0.00000000j
norm src 1.0
norm dest 1.570901
相对误差: 7.21e-04
λ_9 = 1.57080543-0.00000000j
norm src 0.9999999
norm dest 1.5708066
相对误差: 8.78e-04
λ_10 = 1.57096875+0.00000000j
norm src 1.0
norm dest 1.5709695
相对误差: 7.75e-04
λ_11 = 1.57092178-0.00000000j
norm src 1.0
norm dest 1.5709223
相对误差: 7.46e-04
λ_12 = 1.57087958+0.00000000j
norm src 1.0
norm dest 1.5708804
相对误差: 7.56e-04
λ_13 = 1.57092583-0.00000000j
norm src 0.99999994
norm dest 1.5709265
相对误差: 7.78e-04
λ_14 = 1.57090461-0.00000000j
norm src 1.0
norm dest 1.5709051
相对误差: 7.55e-04
λ_15 = 1.57089937-0.00000000j
norm src 0.99999994
norm dest 1.5709003
相对误差: 8.02e-04
λ_16 = 1.57094300+0.00000000j
norm src 1.0
norm dest 1.5709435
相对误差: 6.91e-04
λ_17 = 1.57089722+0.00000000j
norm src 0.99999994
norm dest 1.5708979
相对误差: 7.67e-04
λ_18 = 1.57095349+0.00000000j
norm src 0.99999994
norm dest 1.5709542
相对误差: 6.83e-04
λ_19 = 1.57099140+0.00000000j
norm src 0.9999999
norm dest 1.5709926
相对误差: 7.62e-04
λ_20 = 1.57095301-0.00000000j
norm src 1.0
norm dest 1.5709535
相对误差: 7.53e-04
λ_21 = 1.57089889-0.00000000j
norm src 0.99999994
norm dest 1.5709001
相对误差: 8.01e-04
λ_22 = 1.57089651-0.00000000j
norm src 0.99999994
norm dest 1.5708969
相对误差: 7.64e-04
λ_23 = 1.57086885-0.00000000j
norm src 0.9999999
norm dest 1.5708698
相对误差: 8.17e-04
In [12]:
eigenvalues
Out[12]:
[array(1.5710946+3.2514436e-11j, dtype=complex64),
 array(1.5708753-6.002665e-11j, dtype=complex64),
 array(1.5708374-3.1832315e-12j, dtype=complex64),
 array(1.5707895-3.9847237e-11j, dtype=complex64),
 array(1.5708386+7.298695e-11j, dtype=complex64),
 array(1.5708917-2.989964e-11j, dtype=complex64),
 array(1.5709964+1.1823431e-11j, dtype=complex64),
 array(1.5710214+5.684342e-12j, dtype=complex64),
 array(1.5709006+4.206413e-12j, dtype=complex64),
 array(1.5708054-4.9112714e-11j, dtype=complex64),
 array(1.5709687+6.0936145e-11j, dtype=complex64),
 array(1.5709218-4.5474735e-12j, dtype=complex64),
 array(1.5708796+9.094947e-13j, dtype=complex64),
 array(1.5709258-4.1097792e-11j, dtype=complex64),
 array(1.5709046-9.458745e-11j, dtype=complex64),
 array(1.5708994-2.2509994e-11j, dtype=complex64),
 array(1.570943+4.4110493e-11j, dtype=complex64),
 array(1.5708972+6.366463e-12j, dtype=complex64),
 array(1.5709535+3.6948222e-11j, dtype=complex64),
 array(1.5709914+5.2750693e-11j, dtype=complex64),
 array(1.570953-4.956746e-11j, dtype=complex64),
 array(1.5708989-2.3419489e-11j, dtype=complex64),
 array(1.5708965-5.9117156e-12j, dtype=complex64),
 array(1.5708688-6.366463e-12j, dtype=complex64)]
In [13]:
eigenvectors[0]
Out[13]:
array([ 0.00011019-3.3849868e-05j, -0.00019698-5.8493009e-05j,
        0.00016907-2.1190083e-06j, ...,  0.00023352+1.0564764e-04j,
       -0.00028323-1.2248049e-04j,  0.00031611+6.1884180e-05j],
      dtype=complex64)
In [14]:
eigenvectors[1]
Out[14]:
array([-0.00016843-4.3366521e-04j,  0.0002561 +3.4370035e-04j,
       -0.00010726-4.1487903e-04j, ...,  0.00034043-9.5846306e-05j,
       -0.00050256+1.2186132e-04j,  0.00043388-8.7990644e-05j],
      dtype=complex64)
In [15]:
eigenvectors[2]
Out[15]:
array([-0.00030464+7.2071234e-05j,  0.00022192+1.3316350e-04j,
       -0.00023817-1.4252070e-04j, ..., -0.00026966-1.7527273e-04j,
        0.00020242+1.3561420e-04j, -0.00021154-1.2906564e-04j],
      dtype=complex64)
In [16]:
eigenvectors[3]
Out[16]:
array([-0.00024654+2.6417947e-05j,  0.00020589-1.2865798e-04j,
       -0.00028624+1.0180634e-04j, ...,  0.00030569-2.8551219e-04j,
       -0.00010088+1.4407843e-04j,  0.00020402-2.9525341e-04j],
      dtype=complex64)
In [17]:
eigenvectors[8]
Out[17]:
array([-2.1568088e-04-3.7905786e-05j,  1.1930928e-04+5.8005251e-05j,
       -1.0789587e-04-6.9251844e-05j, ...,  1.4028237e-04-3.2521324e-04j,
        4.8712227e-05+2.4246574e-04j, -2.9026256e-05-2.1543294e-04j],
      dtype=complex64)
In [18]:
eigenvectors[7]
Out[18]:
array([ 0.00032246+1.8667255e-04j, -0.00022841-1.3719682e-04j,
        0.00023254+2.4205162e-04j, ...,  0.00012554+5.5392633e-05j,
       -0.0002477 +1.3193564e-04j,  0.00033989-1.4686681e-04j],
      dtype=complex64)
In [19]:
eigen_index = 8
print("Diff:", cp.linalg.norm(_matvec(eigenvectors[eigen_index]) -
      eigenvalues[eigen_index]*eigenvectors[eigen_index]) / cp.linalg.norm(eigenvectors[eigen_index]))
norm src 1.0
norm dest 1.570901
Diff: 0.0011322624
In [20]:
for i, ev in enumerate(eigenvalues):
    print(f"λ_{i} = {ev:.8f}")
    # 验证本征向量
    v = eigenvectors[i]*1e6
    print(f"v_{i} = {v}")
    w = cp.zeros_like(v)
    w = _matvec(v)
    error = cp.linalg.norm(w - ev * v) / cp.linalg.norm(w)
    print(f"相对误差: {error:.2e}")
    j = i+1
    if i == len(eigenvalues)-1:
        j = 0
    eigen_diff = cp.linalg.norm(
        eigenvectors[i]-eigenvectors[j])/cp.linalg.norm(eigenvectors[i])
    print(f"本征向量{i}与本征向量{j}的相对误差:{eigen_diff:.2e}")
λ_0 = 1.57109463+0.00000000j
v_0 = [ 110.19172 -33.84987j   -196.97662 -58.493008j   169.0651   -2.1190083j
 ...  233.5238 +105.64764j   -283.23187-122.480484j
  316.10928 +61.884182j ]
norm src 1000000.0
norm dest 1571094.6
相对误差: 3.58e-04
本征向量0与本征向量1的相对误差:1.42e+00
λ_1 = 1.57087529-0.00000000j
v_1 = [-168.42702 -433.6652j    256.1002  +343.70035j  -107.259636-414.87903j
 ...  340.42728  -95.846306j -502.56116 +121.86132j
  433.88382  -87.99065j ]
norm src 999999.94
norm dest 1570876.4
相对误差: 8.09e-04
本征向量1与本征向量2的相对误差:1.43e+00
λ_2 = 1.57083738-0.00000000j
v_2 = [-304.6362  +72.071236j  221.92036+133.1635j   -238.16966-142.5207j   ...
 -269.6599 -175.27272j   202.41771+135.6142j   -211.53885-129.06564j ]
norm src 999999.94
norm dest 1570838.0
相对误差: 7.78e-04
本征向量2与本征向量3的相对误差:1.41e+00
λ_3 = 1.57078946-0.00000000j
v_3 = [-246.5437  +26.417948j  205.8921 -128.65797j  -286.23804+101.80634j  ...
  305.6901 -285.51218j  -100.88299+144.07843j   204.02196-295.25342j ]
norm src 999999.94
norm dest 1570790.5
相对误差: 9.31e-04
本征向量3与本征向量4的相对误差:1.41e+00
λ_4 = 1.57083857+0.00000000j
v_4 = [ -40.820797 +30.650171j  121.91324  -85.02151j  -238.41843 +152.1113j
 ...   38.04143 -553.64685j   266.6846  +591.98065j
 -132.45296 -678.05225j ]
norm src 999999.94
norm dest 1570839.6
相对误差: 8.79e-04
本征向量4与本征向量5的相对误差:1.41e+00
λ_5 = 1.57089174-0.00000000j
v_5 = [ -58.202316 +599.9151j     1.9449369-651.8865j   -20.99789  +617.88306j
 ... -141.45654  +489.07758j   -8.781775 -394.24646j
   19.491774 +347.37027j]
norm src 999999.94
norm dest 1570892.5
相对误差: 7.77e-04
本征向量5与本征向量6的相对误差:1.41e+00
λ_6 = 1.57099640+0.00000000j
v_6 = [ 463.5643 -238.84076j  -446.01474+287.80875j   421.00568-253.52501j  ...
 -487.91336 +35.79339j   260.85455-114.044136j -415.89636+101.2075j  ]
norm src 999999.94
norm dest 1570997.5
相对误差: 7.06e-04
本征向量6与本征向量7的相对误差:1.41e+00
λ_7 = 1.57102144+0.00000000j
v_7 = [ 322.45557+186.67255j -228.40799-137.19682j  232.54373+242.05162j ...
  125.53771 +55.39263j -247.69728+131.93564j  339.8872 -146.8668j ]
norm src 999999.94
norm dest 1571022.1
相对误差: 6.51e-04
本征向量7与本征向量8的相对误差:1.42e+00
λ_8 = 1.57090056+0.00000000j
v_8 = [-215.68088  -37.905785j  119.30928  +58.005253j -107.89587  -69.25185j
 ...  140.28236 -325.21326j    48.712227+242.46574j
  -29.026257-215.43294j ]
norm src 1000000.0
norm dest 1570901.1
相对误差: 7.21e-04
本征向量8与本征向量9的相对误差:1.43e+00
λ_9 = 1.57080543-0.00000000j
v_9 = [ 344.97617 -38.126987j -250.47763 +47.23441j   169.48782 -50.32828j  ...
  144.94064-227.73448j  -244.6966 +297.63138j   196.98985-358.6684j  ]
norm src 999999.94
norm dest 1570806.8
相对误差: 8.78e-04
本征向量9与本征向量10的相对误差:1.43e+00
λ_10 = 1.57096875+0.00000000j
v_10 = [-129.90897-381.7529j     93.37714+501.07394j   -65.39111-599.5287j   ...
  655.6552  -21.895672j -683.28925 +12.878436j  680.4141  -72.449005j]
norm src 999999.94
norm dest 1570969.5
相对误差: 7.75e-04
本征向量10与本征向量11的相对误差:1.41e+00
λ_11 = 1.57092178-0.00000000j
v_11 = [-121.22787+695.9635j   182.67911-690.58325j -280.29626+706.19086j ...
  239.62527+104.38387j -414.80487-236.8881j   361.34283+228.88937j]
norm src 1000000.0
norm dest 1570922.2
相对误差: 7.46e-04
本征向量11与本征向量12的相对误差:1.43e+00
λ_12 = 1.57087958+0.00000000j
v_12 = [ -21.943739  -86.00619j    80.26179  +170.22855j
    1.3971834 +52.054836j ... -385.77673   +94.064285j
  622.78265  -113.18395j  -568.748     +45.43582j ]
norm src 999999.94
norm dest 1570880.4
相对误差: 7.56e-04
本征向量12与本征向量13的相对误差:1.41e+00
λ_13 = 1.57092583-0.00000000j
v_13 = [ 158.2305  +145.47247j -104.19043 -227.36905j  245.36418 +164.66583j ...
  -69.85509 +263.15683j  120.93825 -147.52397j -103.269615+101.64767j]
norm src 999999.94
norm dest 1570926.5
相对误差: 7.78e-04
本征向量13与本征向量14的相对误差:1.42e+00
λ_14 = 1.57090461-0.00000000j
v_14 = [ 84.78046  +85.95987j -37.41109 -142.95149j  62.354725+295.85226j ...
  82.32612 -173.09746j -51.33811 +183.3928j   97.629425 -93.42162j]
norm src 1000000.06
norm dest 1570905.1
相对误差: 7.55e-04
本征向量14与本征向量15的相对误差:1.42e+00
λ_15 = 1.57089937-0.00000000j
v_15 = [  -9.087385+134.74391j   -99.95212 -239.5371j     15.379323 +32.093258j
 ... -773.3928  +119.23577j   738.3085  -196.06712j
 -630.05444 +360.8405j  ]
norm src 999999.94
norm dest 1570900.4
相对误差: 8.02e-04
本征向量15与本征向量16的相对误差:1.43e+00
λ_16 = 1.57094300+0.00000000j
v_16 = [-176.36221 -257.47107j   237.45447 +382.26614j  -163.36661 -386.5899j
 ...  -92.916664 +91.919014j  286.11893 -156.5727j
 -158.18794  -43.95432j ]
norm src 1000000.0
norm dest 1570943.5
相对误差: 6.91e-04
本征向量16与本征向量17的相对误差:1.41e+00
λ_17 = 1.57089722+0.00000000j
v_17 = [-167.49866 +277.6496j    41.2842  -143.78377j  -57.657604+248.60416j ...
 -132.83894 +288.1332j   263.88452 -229.12154j -322.7842  +215.67627j]
norm src 1000000.0
norm dest 1570898.0
相对误差: 7.67e-04
本征向量17与本征向量18的相对误差:1.42e+00
λ_18 = 1.57095349+0.00000000j
v_18 = [ 386.8991 +584.85675j -286.46277-569.4879j   296.56204+486.68268j ...
 -298.36572-248.60835j  361.97626+124.00337j -393.24637-276.65213j]
norm src 999999.94
norm dest 1570954.1
相对误差: 6.83e-04
本征向量18与本征向量19的相对误差:1.42e+00
λ_19 = 1.57099140+0.00000000j
v_19 = [-414.9875 -677.5721j    324.04956+589.9055j   -361.40582-604.278j    ...
 -268.78024 -18.964245j  198.30484+171.33107j  -176.90143-139.13943j ]
norm src 999999.9
norm dest 1570992.5
相对误差: 7.62e-04
本征向量19与本征向量20的相对误差:1.40e+00
λ_20 = 1.57095301-0.00000000j
v_20 = [ 131.3372 -377.5479j  -234.77895+379.71188j  338.15387-492.8778j  ...
 -389.25693-346.42773j  369.41122+184.14081j -561.11755-103.37218j]
norm src 999999.94
norm dest 1570953.6
相对误差: 7.53e-04
本征向量20与本征向量21的相对误差:1.44e+00
λ_21 = 1.57089889-0.00000000j
v_21 = [ 203.76662 +444.30246j -105.61026 -412.67868j  233.31195 +246.279j   ...
  -61.440247+353.02307j  245.15659 -395.8376j  -100.93443 +208.14188j]
norm src 999999.94
norm dest 1570900.0
相对误差: 8.01e-04
本征向量21与本征向量22的相对误差:1.43e+00
λ_22 = 1.57089651-0.00000000j
v_22 = [-537.91595-416.83356j  608.7422 +359.76038j -638.08795-454.4591j  ...
  283.41653+203.56702j -446.0495  -64.08735j  423.47617 +74.40231j]
norm src 999999.94
norm dest 1570896.9
相对误差: 7.64e-04
本征向量22与本征向量23的相对误差:1.43e+00
λ_23 = 1.57086885-0.00000000j
v_23 = [ 150.28822  -5.798119j -228.17564 -36.502472j  187.62167+165.91678j  ...
  287.64566+280.93304j  -257.25824-301.7333j    370.39883+179.29327j ]
norm src 999999.9
norm dest 1570869.8
相对误差: 8.17e-04
本征向量23与本征向量0的相对误差:1.42e+00
In [21]:
# qcu.applyEndQcu(set_ptrs, params)